Properties

Label 304.2.i
Level $304$
Weight $2$
Character orbit 304.i
Rep. character $\chi_{304}(49,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $18$
Newform subspaces $6$
Sturm bound $80$
Trace bound $5$

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Defining parameters

Level: \( N \) \(=\) \( 304 = 2^{4} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 304.i (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Newform subspaces: \( 6 \)
Sturm bound: \(80\)
Trace bound: \(5\)
Distinguishing \(T_p\): \(3\), \(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(304, [\chi])\).

Total New Old
Modular forms 92 22 70
Cusp forms 68 18 50
Eisenstein series 24 4 20

Trace form

\( 18 q + 3 q^{3} - q^{5} + 8 q^{7} - 6 q^{9} + O(q^{10}) \) \( 18 q + 3 q^{3} - q^{5} + 8 q^{7} - 6 q^{9} + 4 q^{11} - q^{13} - 9 q^{15} - 5 q^{17} - 6 q^{19} - 4 q^{21} + 7 q^{23} - 6 q^{25} - 18 q^{27} - q^{29} + 24 q^{31} + 2 q^{33} - 4 q^{37} + 2 q^{39} + q^{41} - 7 q^{43} + 12 q^{45} + 7 q^{47} + 2 q^{49} + 11 q^{51} + 3 q^{53} - 3 q^{57} + 19 q^{59} + 19 q^{61} - 24 q^{63} + 6 q^{65} - 19 q^{67} - 30 q^{69} - 19 q^{71} + q^{73} + 52 q^{75} - 40 q^{77} - 31 q^{79} - 17 q^{81} - 52 q^{83} + 9 q^{85} - 78 q^{87} + 3 q^{89} + 40 q^{91} - 20 q^{93} - 13 q^{95} + 17 q^{97} - 12 q^{99} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(304, [\chi])\) into newform subspaces

Label Dim. \(A\) Field CM Traces $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
304.2.i.a $2$ $2.427$ \(\Q(\sqrt{-3}) \) None \(0\) \(-1\) \(1\) \(0\) \(q+(-1+\zeta_{6})q^{3}+(1-\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.b $2$ $2.427$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(-3\) \(0\) \(q+(1-\zeta_{6})q^{3}+(-3+3\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.c $2$ $2.427$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(0\) \(8\) \(q+(1-\zeta_{6})q^{3}+4q^{7}+2\zeta_{6}q^{9}-3q^{11}+\cdots\)
304.2.i.d $2$ $2.427$ \(\Q(\sqrt{-3}) \) None \(0\) \(1\) \(4\) \(0\) \(q+(1-\zeta_{6})q^{3}+(4-4\zeta_{6})q^{5}+2\zeta_{6}q^{9}+\cdots\)
304.2.i.e $4$ $2.427$ \(\Q(\sqrt{-3}, \sqrt{7})\) None \(0\) \(0\) \(-2\) \(-4\) \(q+\beta _{1}q^{3}+(-1+\beta _{1}-\beta _{2})q^{5}+(-1+\cdots)q^{7}+\cdots\)
304.2.i.f $6$ $2.427$ 6.0.2696112.1 None \(0\) \(1\) \(-1\) \(4\) \(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{3}+(\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(304, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(304, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(76, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(152, [\chi])\)\(^{\oplus 2}\)